On square-free values of large polynomials over the rational function field

D. A.N. Carmon, Alexei Entin

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the density of square-free values of polynomials with large coefficients over the rational function field q[t]. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial N as a sum of a k-th power of a small polynomial and a square-free polynomial.

Original languageEnglish
Pages (from-to)247-263
Number of pages17
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume170
Issue number2
DOIs
StatePublished - Mar 2021

Keywords

  • 2010 Mathematics Subject Classification: 11N25 11N32 11N36 11R58 14H05

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